You'll probably want to specify these things
Audio source and bitrate
genre(s) preferred
any types of sound signatures you like (more bass, recessed mids, sharp treble, etc)
if you care about looks, portability, noise leakage, do you care about soundstage, etc etc.
But for an all around alternative to beats a lot of people like the audio technica m50s. There are however tons of different headphones that can be better suited to you than those (heard a lot of good about the beyerdynamic line, dt770, 880, supposed to be a good set of closed cans). You can't really recommend one headphone that suits all since everyone has their own personal preferences. For example I listen to a lot of rock and like the forward sound of grados, but some people despise them for being too shrill (treble high) and too much mids. I could recommend them if you share the same taste as me but they're definitely not the right match for everybody.
My brother bought the audio technica ATH-M30s, and as a casual listener (like I imagine many people who buy beats are) they sound good to him. Not as clear and open sounding as I would like but they work for him. Very portable.
Once you consider other monitoring/high end headphones theres really no reason to go with beats other than their looks (bose as well).
